#### Answer

$\dfrac{4\sqrt{x}+8}{x-4}$

#### Work Step by Step

Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $
\dfrac{4}{\sqrt{x}-2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4}{\sqrt{x}-2}\cdot\dfrac{\sqrt{x}+2}{\sqrt{x}+2}
\\\\=
\dfrac{4\sqrt{x}+8}{(\sqrt{x})^2-(2)^2}
\\\\=
\dfrac{4\sqrt{x}+8}{x-4}
.\end{array}